At the transition from the coverage area of one mobile radio cell to another mobile radio cell in a cellular mobile radio communication system, there may be locations which are not covered by either of the two mobile radio cells or at which the two mobile radio cells overlap only in a small area. The result can be that where a subscriber terminal of a cellular mobile radio communication system changes from one mobile radio cell to another mobile radio cell at such a location, a communication link to the network side of the mobile radio communication system breaks down since the subscriber terminal is located temporarily at a location which is not covered by a base station of the cellular mobile radio communication system, that is to say is located outside the coverage area of both mobile radio cells, or because the area of overlap of the two mobile radio cells is so small that the subscriber terminal passes through this area so quickly that the time for a successful handover procedure from one mobile radio cell to the other mobile radio cell is not sufficient. Such areas of transition between two mobile radio cells occur, for example, on motorways (or highways) at which base stations are placed very closely. It is desirable to provide systems in which it is avoided that link breakdowns occur for the above reasons.